Struggles with the Continuum · HackerPapers discussions

Struggles with the Continuum — mentioned by naasking

Wed, 26 Nov 2025 17:07:49 GMT

Math is a tool for structured reasoning. We often want to reason about things that physically exist. Why should we use a tool that assumes the existence of something that literally cannot physically exist? That introduces the danger that of admitting all sorts of unphysical possibilities into our theories. I think Baez's paper, Struggles with the Continuum, shows a lot of past difficulties we've had that resulted from this: https://arxiv.org/abs/1609.01421

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Struggles with the Continuum — mentioned by naasking

Mon, 18 Nov 2024 15:44:49 GMT

> Can you give some examples? See Baez's paper, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 The UV catastrophe is probably the most well known.

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Struggles with the Continuum — mentioned by naasking

Thu, 14 Mar 2024 18:08:08 GMT

> Here, it is absolutely necessary for QM to work that the unmeasured state is real-valued You're just doubling down on the premise that a theory founded on a formalism based on unbounded numbers requires unbounded numbers to work. Sure, but why is that necessarily reflective of reality? Why does that entail that no other formalism that doesn't embed infinities / continuity is also not possible? I simply see no reason to accept your conclusion. The infinities you see as essential could very well simply be artifacts of our formalisms. In fact, I'd conjecture that our continuous formalisms are…

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Struggles with the Continuum — mentioned by naasking

Thu, 14 Dec 2023 16:13:10 GMT

That was the old thinking. Turns out it leads to divergences which was one of the difficulties that quantum theory overcame. Baez has a good overview of these kinds of problems: Struggles with the Continuum, https://arxiv.org/abs/1609.01421 Lots of issues spring from unphysical assumptions like continuous quantities, point-like objects and infinities. Quantum mechanics was the first step towards more discrete formalisms, and I think future physics will take further steps in this direction to eliminate these issues.

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Struggles with the Continuum — HN submission

Mon, 27 Nov 2023 13:40:06 GMT

Struggles with the Continuum

63 points; 122 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Struggles with the Continuum — mentioned by naasking

Mon, 10 Jul 2023 19:20:18 GMT

> Oh no I get that, but two comments above inciampati was suggesting that we will end up in a situation where some variable will have to have an infinite value The black hole information paradox from that article presumably fits. The conclusion from GR is that no information can escape, which is ultimately incompatible with QM, and that conclusion ultimately depends on the infinite density of the singularity. I think the more charitable reading is that we'll find situations where either no sensible calculation can be done, or the sensible calculations we do churn out nonsense. Divergence in…

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Struggles with the Continuum — mentioned by naasking

Mon, 10 Jul 2023 17:32:33 GMT

> But when they tried to quantize gravity, they ran into unnatural infinities that had to be sidestepped with clumsy mathematical tricks. Maybe they run into unnatural infinities because all of our formalisms in physics are still fundamentally continuous rather than discrete. Uncountable infinities are baked right into the foundations of how we use reason about these systems, so infinities will naturally result. Physics has repeatedly had to tame infinities by elaborate tricks, or by eliminating them entirely [1]. Some people are increasingly looking to discrete formalisms, and I think this…

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Struggles with the Continuum — mentioned by naasking

Sat, 25 Feb 2023 01:24:51 GMT

Nobody knows of any certain reasons to not scale, but there's plenty of speculation. Someone else posted about Gil Kalai in this subthread, so he's one high profile person that has documented his skepticism on quantum computing and explained his reasons. For my part, I don't think quantum foundations are on a firm footing. I think the measurement problem is still unresolved to a satisfactory degree, which means our understanding of decoherence is incomplete. Per the link I posted above, there's also a good chance that gravity is inherently decoherent, which means entanglement will naturally…

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Struggles with the Continuum — mentioned by naasking

Mon, 20 Feb 2023 15:31:37 GMT

Yes, there are historical issues with that calculation, and field theories in general. I've become very suspicious of continuous formalisms period: https://arxiv.org/abs/1609.01421 I think many problems in physics will be solved by moving to more discrete formalisms.

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Struggles with the Continuum — mentioned by naasking

Wed, 15 Feb 2023 13:26:47 GMT

> As far as we know, time and space are continuous. Our models are continuous. The map is not the territory. > Various aspects of quantum field theories would not work in a discretized universe. If you're referring to symmetries, that's not true [1]. Discretized theories have received barely any attention because physicists have simply built upon the formalisms they're used to from classical physics. We see people frequently saying that we should abandon classical intuitions now that we have quantum mechanics, but we haven't really even tried to abandon classical formalisms, which are just…

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Struggles with the Continuum — mentioned by naasking

Sun, 08 Jan 2023 15:43:55 GMT

First, all of physics is computable to arbitrary precision. Continuous quantities in physics are being systematically removed because they almost inevitably introduce absurdities [1]. Measures lose all meaning below Planck length anyway. Second, the point of enumerating all Turing machines is not to run them to completion, it's simply to create them, so your objection is inapplicable. The Turing machine itself defines an ontology. The claim was that algorithms do not have access to novel ontologies, which conflicts with the basic construction of recursively enumerable functions that defines…

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Struggles with the Continuum — mentioned by naasking

Wed, 07 Dec 2022 02:31:41 GMT

Nice list! I'll add one more I enjoyed: Struggles with the Continuum, by John Baez, https://arxiv.org/abs/1609.01421

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Struggles with the Continuum — mentioned by throwaway81523

Sat, 19 Nov 2022 22:01:07 GMT

There are all kinds of blow-ups in Newtonian mechanics and in other equations of physics. The singularity at the center of a black hole in general relativity is a famous example. The ultraviolet catastrophe in classical thermodynamics was another. The presumption is that blow-ups in an equation indicate a mismatch between the equation and the true physical world, telling physicists to look for better theories, whose equations don't blow up. For the ultraviolet catastrophe, the mystery was solved through the discovery of quantum mechanics. For GR, it is still unsolved, and the solution is…

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Struggles with the Continuum — mentioned by macrolocal

Wed, 29 Sep 2021 23:59:45 GMT

As an aside, this idea that reality is "geometrical" leads to all kinds of fascinating paradoxes[1]. [1] https://arxiv.org/abs/1609.01421

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Struggles with the Continuum — mentioned by raattgift

Tue, 20 Jul 2021 10:27:54 GMT

In an accelerating expanding universe like the one we appear to occupy (and the one modelled by our current "concordance" standard model of comology), the comoving horizon is at constant comoving distance. Cast into more Earth-centric coordinates, it is at a finite spatial distance at all finite times. However, there is no reason to expect that a timelike worldline rooted at "here and now" (converting a chosen comoving coordinate into the origin of spherical coordinates for a Eulerian observer) cannot be extended into the infinite future, and at +infinite time the horizon will be at an…

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Struggles with the Continuum — mentioned by OscarCunningham

Thu, 29 Mar 2018 18:10:58 GMT

John Baez's "Struggles with the Continuum" (https://arxiv.org/pdf/1609.01421.pdf) covers similar topics in more detail.

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Struggles with the Continuum — HN submission

Sun, 07 Jan 2018 20:57:56 GMT

Struggles with the Continuum

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Struggles with the Continuum — HN submission

Mon, 11 Dec 2017 04:03:33 GMT

Struggles with the Continuum – John Baez

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Struggles with the Continuum — mentioned by mikhailfranco

Wed, 12 Apr 2017 08:59:06 GMT

For the parallel historical development of 'the continuum' in physics, I recommend this readable survey: Paper: https://arxiv.org/abs/1609.01421 https://math.ucr.edu/home/baez/continuum.pdf Blog summary with discussion: https://johncarlosbaez.wordpress.com/2016/09/08/struggles-wi... https://johncarlosbaez.wordpress.com/2016/09/09/struggles-wi...

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Struggles with the Continuum — mentioned by j2kun

Sat, 07 Jan 2017 07:32:56 GMT

Try this physics paper[1] explaining how pretty much every model we have of physics is broken in fundamental ways. Things you take for granted because of what you've read in popular media (eg., heat death of the universe) are simply speculation based on stretching an incomplete mathematical model to its limits. The simulated reality nonsense is the same bad logic in a different guise. [1]: https://arxiv.org/abs/1609.01421

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Struggles with the Continuum — HN submission

Wed, 07 Sep 2016 09:56:54 GMT

Struggles with the Continuum

73 points; 9 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Struggles with the Continuum — mentioned by raattgift

Wed, 07 Sep 2016 09:55:45 GMT

dS space is really simple; you only need a cosmological constant to power a uniform metric expansion, and no matter to retard it. The far future dS space approximation has only localized matter, namely mostly isolated gas molecules and (swarms of) black holes, each occupying their own Hubble volume, as all their non-gravitationally-bound neighbours have disappeared across the horizon. Unless something really unexpected arises to retard the metric expansion of space -- and many working scientists are looking for that, since it would be amazingly cool -- that we see right back to the surface of…

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